Dimethyl Sulfoxide

Dec 29, 2008 - State Key Laboratory for Chemical Fibers Modification and Polymer Materials, Donghua University, Shanghai 201620, China; College of Mat...
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J. Phys. Chem. B 2009, 113, 603–609

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ARTICLES Viscoelastic Behavior of Polyacrylonitrile/Dimethyl Sulfoxide Concentrated Solution during Thermal-Induced Gelation Lianjiang Tan, Shuiping Liu, and Ding Pan* State Key Laboratory for Chemical Fibers Modification and Polymer Materials, Donghua UniVersity, Shanghai 201620, China; College of Materials Science and Engineering, Donghua UniVersity, Shanghai 201620, China ReceiVed: NoVember 3, 2008; ReVised Manuscript ReceiVed: NoVember 22, 2008

Thermal-induced gelation of polyacrylonitrile (PAN)/dimethyl sulfoxide (DMSO) concentrated solution has been rheologically investigated in relation to temperature and aging. Phase behavior of PAN/DMSO solution was studied through examining the intrinsic viscosities [η]. The gelation temperature Tg, gel time tg, and the critical values of relaxation exponent n were obtained by measuring the viscoelastic functions (G′, G′′, tan δ, and η*) based on the Winter and Chambon theory. The solution with higher PAN concentration was found to be more sensitive to the temperature, which makes it gel at a higher temperature. The n value, however, changes little with varied concentration. The gel strength S was found to depend on the concentration of the solution. Gelation of the 23 wt % PAN/DMSO solution occurs after being aged at 25 °C for a period of time, i.e., gel time tg. The critical n value (S value) at tg was larger (smaller) than that at Tg in the cooling process, attributed to the different critical feature of the PAN gels formed in different conditions. The power law relations η0 ∝ ε-γ and Ge ∝ εz were found to be valid for PAN/DMSO solution before and beyond the gel time tg, respectively. η0 ∝ ε-γ,

Introduction Gelation, or sol-gel transition, corresponds to a phenomenon by which a cross-linking polymeric material undergoes a phase transition from a liquid to a solid state. A three-dimensional network is formed, and beyond the gel point, its firmness continues to increase with increasing cross-linking density. Physical gelation is the process of cross-linking which reversibly transforms a solution of polymer into a gel. Contrary to chemical bonds, the energy level of physical junctions is low and the junctions are easy to be broken via, for instance, increasing temperature or adding solvent. For thermoreversible gels, thermal-induced gelation is the most common gelation mechanism and has been extensively studied by many researchers.1-3 Dynamic rheology is one of the most powerful tools to monitor gelation and microstructural changes in polymer materials, and the viscoelastic behavior of polymer gels near the sol-gel transition has been extensively studied.4-7 The viscoelastic functions such as dynamic storage modulus G′, loss modulus G′′, loss tangent tan δ, and complex viscosity η* measured through dynamic shear tests are very sensitive to the structural changes during the formation of a polymer gel. The rheological characteristics in the vicinity of the sol-gel transition can be described using the power laws or scaling laws. The zero-shear viscosity η0, dynamic moduli G′ and G′′, and equilibrium modulus Ge measurable before, at, and beyond the gel point can be expressed by three power laws,8-13 which have been extensively applied to many types of polymeric gels: * Corresponding author: e-mail [email protected]; Tel 86-02167792937; Fax 86-021-67792937.

p < pg

G'(ω) ∼ G''(ω) ∼ ωn, Ge ∝ εz,

p ) pg

p > pg

(1) (2) (3)

where ε ) |pg - p|/pg is the relative distance of a variable from the gel point pg. pg denotes the point where there is nonzero probability that a randomly chosen molecular chain exhibits infinite molecular weight;14 p represents the extent of gelation and can be in terms of the degree of cross-linking, gel time, gelation concentration, gelation temperature, etc.; ω is the angular frequency; γ, n, and z are the power exponents determining the critical characteristics in the vicinity of sol-gel transition.15 Ge is in fact the quasi-equilibrium modulus due to the extreme difficulty in obtaining the actual equilibrium modulus of physical gels.16 The main chemical characteristic of PAN is the presence of a permanent dipole in the monomer unit caused by the bulky CN group with strong polarity. This makes the gelation of PAN solutions possible if proper solvents (e.g., dimethylformamide, dimethyl sulfoxide, etc.) are used. Rheological properties and gelation of concentrated PAN solutions are not much studied and are thus fertile ground of scientific research due to the industrial importance of PAN-related materials (most wellknown PAN-based carbon fiber17-19). In the present article, we measured the rheological behaviors of PAN/DMSO concentrated solutions to investigate the dynamic viscoelastic properties of PAN gels during gelation caused by decreasing temperature and

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aging at constant temperatures. The validity of the power law was also examined for gelation of the PAN/DMSO solutions. Experimental Methods Materials. PAN copolymers (acrylonitrile:itaconic acid ) 98: 2) were provided by Shanghai Institute of Synthetic Fiber (Shanghai, China) with a viscosity-average molecular weight Mη ) 7.8 × 104 g mol-1. DMSO (analytically pure) was purchased from Shanghai Wulian Chemical Industry Co. Ltd. (Shanghai, China), and deionized water was used in the whole study. Viscometric Measurements. Several dilute PAN/DMSO solutions (the polymer concentration in the range of (1.0s4.0) × 10-3 g/mL) were prepared by mixing a small amount of PAN copolymer with DMSO at 50 °C. Viscosities of the solutions were measured at a series of temperatures within 10s60 °C using an Ubbelohde capillary viscometer. All the measurements were carried out in a thermostat maintained within (0.01 °C of the desired temperature. The Huggins and Kraemer equations were used to determine the intrinsic viscosities [η]:20

ηsp ) [η] + kH[η]2c c

(4)

ln ηr ) [η] - kK[η]2c c

(5)

where ηsp is the specific viscosity, ηr is the relative viscosity, c is the polymer concentration with units of g/mL, and kH and kK are the Huggins and Kraemer constants, respectively. Preparation of Concentrated PAN/DMSO Solutions. A certain amount of PAN copolymers was dispersed in DMSO in a three-neck bottle. The resulting slurry was left swollen at 50 °C for 2 h and at 60 °C for another 2 h, stirred by an electric paddle stirrer. Subsequently, it was stirred again at 70 °C for an additional 6 h to produce a viscous PAN/DMSO solution. Two such solutions with PAN concentrations of 20 and 23 wt %, respectively, were prepared. The solutions were then deaerated for 3 h in a vacuum drying oven at 70 °C. Rheological Characterization. The dynamic rheological measurements were conducted using an advanced solution and melt rotation rheometer (ARES-RFS, TA) equipped with two parallel plates. The temperature control was done with a thermostatic bath within (0.1 °C of the preset value. The parallel plate on which samples (the PAN solutions) were placed was 25 mm in diameter, and the sample size was 2 mm. A thin layer of low-viscosity paraffin oil was applied to cover the exposed surface of the samples, protecting them from dehydration or evaporation and thus minimizing the testing errors. The details of the rheological experiments were as follows: (1) Strain sweep at different temperatures was conducted over the oscillation frequencies from 0.1 to 100 rad/s to obtain the linear viscoelastic regime of the samples. 1% was chosen as the strain amplitude in all the dynamic measurements. (2) Temperature sweep from 70 to 30 °C with the cooling rate of 1 °C/min at three constant frequencies (1, 6.3, and 56.7 rad/s) was used to trace the loss tangent tan δ against temperature during the gelation process of the samples. (3) Time sweep for the 23 wt % PAN sample at different constant temperatures (55, 40, and 25 °C) and a constant frequency (6.3 rad/s) was aimed to determine the influence of the gelation process on the dynamic viscoelastic parameters (G′, G′′, η*). (4) A frequency sweep at five constant temperatures (65, 55, 45, 25, and 15 °C) for the

Figure 1. Temperature dependence of the intrinsic viscosity [η] for PAN/DMSO solution.

samples was performed to examine the temperature effect on the dynamic viscoelastic parameters (G′, G′′, tan δ) over a wide range of frequency and temperature. Another frequency sweep for the 23 wt % PAN sample aged at 25 °C for different time was conducted to examine the dynamic viscoelastic parameters (G′,G′′, η*) during the aging process. Each rheological test was performed twice to reduce the experimental errors and ensure the reproducibility of the measurements. Results and Discussion Intrinsic Viscosity and Phase Behavior. It is shown in Figure 1 that the intrinsic viscosity [η] first increases and then decreases with increased temperature, reaching a maximum at 28 °C. This means that the PAN/DMSO interaction is strongest at 28 °C, and the dimension of PAN coils is at a maximum. At the temperatures below 28 °C, the interaction between PAN molecular chains and DMSO is weaker. The contacts among the molecular chains and segments increase by either the contraction of individual coils or the interpenetration of different coils, leading to chain aggregation and thus macroscopic phase separation. When the temperature exceeds 28 °C, PAN chains tend to separate apart and the PAN/DMSO solution is always homogeneous without phase separation. Since there exists an upper critical solution temperature (UCST) for PAN/DMSO solutions,21 Tc ) 28 °C can be regarded as the UCST. If gelation occurs at a temperature above Tc, the resultant gel is homogeneous and transparent. In contrast, phase separation may precede gelation below Tc, which results in a turbid gel. Dependence of Viscoelastic Behavior on Temperature. Winter and Chambon have proposed that the crossover point of storage modulus G′ and loss modulus G′′ can be considered as the inception of the gelation process.22 However, it has also been reported in the literature that for some systems the crossover of G′ and G′′ is not a reliable criterion for determination of gel point Tg due to its high dependence on testing frequency.23,24 Another criterion based on the temperature dependence of the loss tangent tan δ at different oscillation frequencies can be used;25 i.e., Tg is the temperature at which tan δ becomes frequency independent, and all curves at different oscillation frequencies coincide at the point. Furthermore, at this point both G′ and G′′ were found to follow a power-law behavior as defined by eq 2. The loss tangent tan δ can then be expressed as26

Viscoelastic Behavior of PAN/DMSO Concentrated Solution

tan δ ) G''(ω)/G'(ω) ) tan(nπ/2) ) const

(6)

The value of the critical relaxation exponent n strongly depends on molecular and structural details of the system. The shear stress relaxation modulus G(t) is known to obey a power law at the gel point:27,28

G(t) ∼ St-n

(0 < n < 1)

(7)

where S is the gel strength with an unusual unit of Pa · sn and n is the relaxation exponent. A similar expression which relates G′(ω) and G′′(ω) to S and n at the gel point is more convenient to use for determination of the value of S:29

G'(ω) ) G''(ω)/tan δ ) SωnΓ(1 - n) cos(nπ/2)

(8)

Here Γ(1 - n) is the gamma function. According to Winter and Mours,15 stiffer gels at the critical point usually have a small n value (0 r n < 0.5) and a larger strength factor S, while a larger n (0.5 < n f 1) corresponds to a softer and weaker gel with a smaller S. To determine the critical gel point and the specific values of n and S based on the frequency criterion, temperature sweep tests for the PAN/DMSO solutions at three oscillation frequencies were carried out. We can see in Figure 2 that three curves of tan δ at different frequencies cross over at a point, which is considered as the gelation temperature Tg. The sol-gel transition occurs at this temperature, and a fractal gel gradually forms with the further decrease of temperature. The gel point Tg of the 23 wt % PAN/ DMSO solution is 51.8 °C, higher than that of the 20 wt % PAN/DMSO solution, 45.6 °C, due most likely to the lower chain mobility resulted from more entanglements at high concentration. More importantly, the n values of the two solutions calculated from the critical values of the loss tangent tan δ using eq 6 are 0.623 and 0.605, respectively. The n value within a certain range indicates a corresponding mechanism of chain aggregation and cluster growth. The slight difference between the two n values reflects the unique structure of the critical gel at Tg, taking experimental error into consideration. The S values for the two solutions calculated from the G′ and G′′ data at their own gel points based on eq 8 are 172.56 ( 7.53 Pa · s0.623 and 189.91 ( 8.92 Pa · s0.605, respectively. In general, S rises while the cross-linking density of the gel network decreases.30 The larger S value of the 23 wt % PAN/DMSO solution is ascribed to the larger mass of PAN in the solution. Values of tan δ as a function of ω for the two PAN/DMSO solutions at various temperatures are shown in Figure 3. The tan δ value decreases with the decrease of temperature for both solutions, explained by a lower viscous/elastic ratio when the temperature is lower. Furthermore, the tan δ curve of the 20 wt % PAN/DMSO solution exhibits a frequency-independent plateau at 45 °C in the frequency range, indicating the occurrence of gelation at this temperature. It is also noted that 45 °C is very close to the critical gel point Tg of the solution obtained in the temperature sweep discussed above. For the 23 wt % PAN/DMSO solution, the tan δ curve becomes nearly frequency independent at 55 °C, which is also in the vicinity of the Tg of this solution. The tan δ curves for the temperatures either higher or lower than Tg behave differently, since the solutions are either in sol or gel states. Figure 4 shows the storage modulus G′ and loss modulus G′′ as a function of frequency ω at different temperatures for the two PAN/DMSO solutions, following the commonly

J. Phys. Chem. B, Vol. 113, No. 3, 2009 605 observed relations G′(ω) ∼ ωn′ and G′′(ω) ∼ ωn′′. For the 20 wt % PAN/DMSO solution, G′′ dominates the viscoelastic properties over the entire frequency range at high temperature, an indication of viscoelastic fluid before the sol-gel transition occurs. With the decrease of temperature, both G′ and G′′ increase, with G′ at a higher rate than G′′. Also, the two moduli become less frequency dependent at lower temperatures, since more “permanent” cross-linking points formed among the molecular chains lead to a network less sensitive to the frequency or time scale change. When the temperature is low enough, G′ becomes predominant, indicative of the formation of an elastic gel. More importantly, G′ and G′′ are linear with the frequency and parallel to each other at 45 °C, signifying the occurrence of sol-gel transition at this temperature. Similar dynamic viscoelastic behaviors were observed for the 23 wt % PAN/DMSO solution, except that G′ and G′′ exhibit approximate linearity at a higher temperature, 55 °C. This reveals the strong dependence of gelation temperature on the concentration of the solution, which can be explained as follows: as concentration grows, the trend of chain aggregation or entanglement increases, resulting in easier gelation; i.e., the sol-gel transition of PAN/DMSO solution occurs at elevated temperature where the chain mobility is larger. Figure 5 shows the temperature dependence of n′ (exponent of G′ versus ω) and n′′ (exponent of G′′ versus ω) for the two PAN/DMSO solutions. In both cases, n′ and n′′ show a significant temperature dependence; i.e., n′ and n′′ decrease with decreased temperature. The two curves intersect at a temperature where n′ ) n′′ ) nc. The crossover temperatures for the two PAN/DMSO solutions are about 45.5 and 52.5 °C, respectively, in good agreement with the gel point Tg values determined from the aforementioned tan δ versus temperature data. The critical value nc represented by the value of n′ and n′′ at the gel point also agrees well with that obtained from the tan δ versus temperature data for both solutions, showing again the unique gel structure formed in such conditions. Dependence of Viscoelastic Behavior on Aging Time. Monitoring the variation of viscoelastic functions such asG′, G′′, and η* as a function of aging time at different constant temperatures is a good way to rheologically study the kinetics of thermal-induced gelation. Accurate determination of the gelation temperature Tg of PAN/DMSO solution is a prerequisite for the investigation. We have known from the last section that the gelation temperature of the 23 wt % PAN/DMSO solution Tg ) 51.8 °C, which means gelation of this solution above 51.8 °C is extremely difficult. So the time evolution of the viscoelastic properties during gelation process was investigated at three temperatures either around or below Tg. Isothermal aging time dependence of dynamic storage modulus G′ at different temperatures and a constant frequency ω ) 6.3 rad/s is shown in Figure 6. At 25 and 40 °C, a drastic increase in G′ with aging time was clearly observed. The value of G′ levels off and reaches a plateau (equilibrium modulus Ge) at long times as a result of formation of an elastic gel. The time at which G′ levels off was found to decrease with decreased temperature, attributed to the quicker gelation process at lower temperature. At 55 °C, the rate of gelation is significantly reduced, demonstrated by the disappearance of the plateau within the data range of aging time. This implies that a much longer aging time is needed for the solution to gel at a temperature around the gelation temperature Tg. G′′ and η* exhibit similar behavior, as can be seen in Figures 7 and 8. Like the behavior of with time and temperature discussed above, G′′ and η* increase with aging time and reach

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Figure 2. Loss tangent tan δ versus temperature in the cooling process at various frequencies for the 20 and 23 wt % PAN/DMSO solutions.

Figure 3. Loss tangent tan δ as a function of frequency ω at various temperatures for the 20 and 23 wt % PAN/DMSO solutions.

Figure 4. Storage modulus G′ and loss modulus G′′ as a function of frequency ω at different temperatures (15, 30, 45, 55, and 60 °C from top to bottom) for the 20 wt % PAN and 23 wt % PAN/DMSO solutions. The data were shifted along the vertical axes by 10a to avoid overlapping.

an equilibrium value in the terminal region at the two lower temperatures. Although G′′ and η* also increase with the evolution of aging process at 55 °C, they never reach a plateau in the data range because the rate of gelation is very small. Figure 9 shows the frequency dependence of G′ and G′′ at different time intervals for the 23 wt % PAN/DMSO solution at 25 °C, a temperature far below the gelation temperature Tg. It is obvious that G′ and G′′ increase with both aging time and frequency. At a given aging time, low frequencies correspond to smaller G′ and G′′, showing that polymer solutions or gels

behave more like liquids. When the frequency increases to high values, the solutions or gels become more solidlike since the rate of oscillation exceeds the time scale of molecular rearrangements. The dependence of G′ and G′′ on frequency becomes less and less apparent with the aging time, indicating that the solution gradually changes from sol state to gel state. The frequency dependence of η* for different aging times is shown in Figure 10. η* is found to be functions of both aging time and frequency. At a certain frequency, η* increases with the aging time, indicating mutative viscoelastic properties of

Viscoelastic Behavior of PAN/DMSO Concentrated Solution

J. Phys. Chem. B, Vol. 113, No. 3, 2009 607

Figure 5. Temperature dependence of the exponents n′ and n′′ obtained from linearly fitting the frequency dependence data of G′ and G′′ in Figure 4 according to eq 2.

Figure 6. Time dependence of storage modulus G′ of the 23 wt % PAN/DMSO solution at a constant frequency 6.3 rad/s for different temperatures.

Figure 7. Loss modulus G′′ of the 23 wt % PAN/DMSO solution at a constant frequency 6.3 rad/s for different temperatures.

the solution. During the whole aging process, η* decreases with increased frequency, typical of shear thinning effect. The time dependence of n′ (exponent of G′ versus ω) and n′′ (exponent of G′′ versus ω) is depicted in Figure 11. Both n′ and n′′ decrease with the aging time and cross over at the time of 1292 min, which is defined as the gel time tg. At the aging time of 400 min, the n′ value exceeds 1, indicating that the solution has been in the process of gelation but is still in sol state. n′ and n′′ have the same value of around 0.72 at the gel point tg. This value reflects the critical gel structure when the sol-gel transition occurs. Beyond tg, both n′ and n′′ decrease

Figure 8. Complex viscosity η* of the 23 wt % PAN/DMSO solution at a constant frequency 6.3 rad/s for different temperatures.

faster, with n′′ being larger than n′, implying the formation of an elastic gel. We notice that the n value (around 0.72) of the gel formed during an aging process is larger than those of the gels formed in a cooling process. Further calculation shows that the gel strength S value is 148.62 ( 15.60 Pa · s0.72, smaller than that (189.91 ( 8.92 Pa · s0.605) for the same solution in the cooling process. These phenomena may be explained as follows. Gelation of an aged solution needs a relatively long period of time, during which the fractal clusters gradually grow. The solution reaches the sol-gel transition with less cross-linking points in it, and the resultant critical gel is thus weaker, leading to larger n and smaller S. Whereas gelation of a solution in a cooling process occurs within a short time. The rapid growth of the fractal clusters leads to the formation of more crosslinking points, producing a stronger critical gel. In addition, the aging of the solution proceeded at 25 °C, lower than the critical temperature Tc ) 28 °C. The sol-gel transition may be accompanied by phase separation, resulting in a weaker turbid gel. As for industrial application such as PAN fiber spinning, quick thermal-induced gelation is preferred in order to obtain fibers with better mechanical properties. Power Law for PAN Solution before and beyond the Gel Point during Aging Process. The power law relations expressed by eqs 1 and 3 can be used to investigate the viscoelastic behavior of the 23 wt % PAN/DMSO solution before and beyond the gel point during the aging process. For this purpose, the following relationship in this study is suggested:

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Figure 9. Storage modulus G′ and loss modulus G′′ as a function of frequency ω at different aging times for the 23 wt % PAN/DMSO solution at 25 °C.

Figure 10. Complex viscosity η* as a function of frequency ω at different aging times for the 23 wt % PAN/DMSO solution at 25 °C.

Figure 12. Zero-shear viscosity η0 versus the relative distance for the 23 wt % PAN/DMSO solution during the aging process at 25 °C.

Figure 12 depicts the relation between the zero-shear viscosity η0 and the relative distance ε before the gel point. The η0 values are the η* values before the gel point at a very low frequency (0.4 rad/s). The linear fit of the η0 values gives a slope of -0.32, from which we obtain γ ) 0.32. Figure 13, on the other hand, shows the equilibrium modulus Ge as a function of ε. Ge is in practice obtained from the G′ value beyond the gel point at the frequency of 0.4 rad/s, since a complete stress relaxation is more readily realized at a low frequency. The experimental data fall on a straight line with a slope of 0.79, that is, z ) 0.79. The exponent n can be determined from the critical values of γ and z via the equation7,32,33

n ) z/(z + γ) Figure 11. Time dependence of the exponents n′ and n′′ obtained from linearly fitting the frequency dependence data of G′ and G′′ in Figure 9 according to eq 2.

p t ≈ pg tg

(9)

(11)

The critical values of γ and z (0.32 and 0.79, respectively) yield a value of n ) 0.712, which is in good accordance with that obtained from the power law of G′ and G′′ at the gel point tg. Conclusions

and the expression of ε is thus

ε ) |t - tg |/tg

(10)

That is, when close to the gel point, the meaning of power law in terms of time should be the same as the percolation expressions (p and pg).31

The phase behavior of PAN/DMSO solution was analyzed by observing the changes of intrinsic viscosities [η] with temperature. A critical temperature Tc ) 28 °C was regarded as the UCST below which phase separation may occur. The dependence of viscoelastic behavior of PAN/DMSO solutions on temperature and aging time was rheologically investigated through measurements of the viscoelastic functions such as G′,

Viscoelastic Behavior of PAN/DMSO Concentrated Solution

J. Phys. Chem. B, Vol. 113, No. 3, 2009 609 Acknowledgment. This work was supported by grants from the National Basic Research Program (973 Program) (2006CB606505), the Shanghai Fundamental Theory Program (07DJ14002), the National Natural Foundation of China (50333050), the Programme of Introducing Talents of Discipline to Universitie No. 111-2-04 and the Shanghai Leading Academic Discipline Project (B603). References and Notes

Figure 13. Equilibrium modulus Ge versus the relative distance for the 23 wt % PAN/DMSO solution during the aging process at 25 °C.

G′′, tan δ, and η*. In a cooling process, the gelation temperature Tg was obtained from the crossover point of the tan δ versus temperature curves at various frequencies. The gelation of the 23 wt % PAN/DMSO solution is more sensitive to the temperature than the 20 wt % PAN/DMSO solution, demonstrated by a higher Tg. However, the relaxation exponent n value calculated from the tan δ value at the crossover point changed little for the two solutions, indicating the unique nature of the critical gel regardless of the PAN concentration. These results were verified by the tan δ versus ω and G′, G′′ versus ω data. The gel strength S increased with the increase of PAN concentration in the solution. Moreover, G′ and G′′ were found to follow a power law relation as a function of frequency with exponents n′ and n′′ that are strongly dependent on temperature. The Tg value and the critical n value determined from the temperature at which the exponents n′ and n′′ coincide were found to be identical to the values obtained from the tan δ versus temperature data. Aging at a temperature below Tg gives rise to gelation of PAN/DMSO solution. The time at which the sol-gel transition occurs can be defined as the gel time tg. G′, G′′, and η* are functions of both aging time and frequency. The power law relation as a function of frequency is applicable to G′ and G′′ at tg. The value of tg determined from the crossover of the exponents n′ and n′′ was 1292 min. There are differences between the critical n values and S values obtained during the aging process and in the cooling process, ascribed to the different critical structure and strength of the PAN gels formed in these two cases. The value of n calculated using the relation n ) z/(z + γ) is in accordance with that obtained from the n′ and n′′ versus aging time curves.

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